Factorisation Test

Result

Factorisation Test - 6

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

The factorisation of is

A

B

C

D

Solution
Question 2
1 / -0

If (x² + x + 4) (x² - x + 4) = p² - q², then what is the value of p?

A
(x² + x)

B
(x + 4)

C
(x² + 4)

D
(x² - x)

Solution

(x² + x + 4) (x² - x + 4)
= [(x² + 4) + x] [(x² + 4) - x]
= (x² + 4)² - x²[Using (a + b)(a - b) = a²- b²]
Now, (x² + 4)² - x² = p² - q²
∴ p = (x² + 4)
Question 3
1 / -0

The factors of are

A

B

C

D

Solution

Using the property, (a + b)(a - b) = a² - b²
Question 4
1 / -0

The factors of 25t² - 5t - 12 are

A

B

C

D

Solution
Question 5
1 / -0

The factors of are

A

B

C

D
None of the above

Solution

We know that

Again, we will use the identity on .

We get

So, we have

=
Question 6
1 / -0

The factors of are

A

B

C

D

Solution

[Using a² + b² + 2ab = (a + b)²]
Question 7
1 / -0

The factors of are

A

B

C

D

Solution

We know that
So,

Again, we will apply the same identity of .
Question 8
1 / -0

On factorising , we get

A

B

C

D

Solution

We know that

So,
Question 9
1 / -0

The factors of are

A

B

C

D
None of these

Solution

[Using a² + b² - 2ab = (a - b)²]

[Using (a² - b²) = (a + b)(a - b)]
Question 10
1 / -0

Which of the following options is the same as (x + 2)² – 6(x + 2) + 9?

A
(x + 5)(x – 1)

B
(x – 5)(x + 1)

C
(x – 1)(x – 1)

D
(x + 1)(x – 1)

Solution

(x + 2)² - 6(x + 2) + 9
Put x + 2 = a .........(1)
a² - 6a + 9
= a² - 3a - 3a + 9
= a(a - 3) - 3(a - 3)
= (a - 3)²
Put the value of 'a' from (1).
= [(x + 2) - 3]²
= [x + 2 - 3]² = (x - 1)² = (x - 1)(x - 1)
Question 11
1 / -0

One of the factors of is

A

B

C

D

Solution
Question 12
1 / -0

On dividing by , we get

A

B

C

D

Solution

=
Question 13
1 / -0

One of the factors of (x + 2)(x² + 25) - 10x(x + 2) is

A
(x - 5)

B
(x + 5)

C
(x - 10)

D
(x + 10)

Solution

(x + 2)(x² + 25) - 10x(x + 2)
Taking (x + 2) common from both the terms,
(x + 2) [x² + 25 - 10x]
= (x + 2) [x² - 10x + 25]
= (x + 2) [x² - 25 - 10x]
= (x + 2) [x² - 10x + 25]
= (x + 2) [x² - 5x - 5x + 25]
= (x + 2) [x(x - 5) - 5 (x - 5)]
= (x + 2) (x - 5) (x - 5)
Question 14
1 / -0

Factorise:

A

B

C

D

Solution

Let

We get

Now,
Question 15
1 / -0

Simplify:

A

B

C

D

Solution

... (1)

First we will solve only the numerator.

Putting this value in (1),

=
Question 16
1 / -0

Which of the following is/are the factor(s) of ?

(i)
(ii)
(iii)

A
Only (ii)

B
Only (i)

C
Only (iii)

D
Both (i) and (ii)

Solution
Question 17
1 / -0

Fill in the blanks:

(i) is equal to___P____.

(ii) is equal to ____Q____.

(iii) When we divide by , the resultant is kbc - a. Then, k = ____R___.

A
P = , Q = 12y + 2, R = 2

B
P = , Q = 12y + 1, R = 0

C
P = , Q = 12y - 2, R = 5

D
P = , Q = 12y, R = 3

Solution

(i) = =
= P

(ii) = = 12y + 2 = Q

(iii) = = (2bc - a) = kbc - a

So, k = 2 = R
Question 18
1 / -0

Which of the following statements is incorrect?

A
For factorising an algebraic expression of the type x² + px + q, we find two factors a and b of q (i.e. the constant term) such that ab = q and a + b = p.

B
"Division is the inverse of multiplication." This statement is true only in case of numbers, but it does not apply in case of division of algebraic expressions.

C
When we factorise an algebraic expression, we write it as a product of factors, where these factors may be numbers, algebraic variables or algebraic expressions.

D
When we multiply the expression enclosed in a bracket by a constant (or a variable) outside, each term of the expression has to be multiplied by the constant (or the variable).

Solution

(1) For factorising an algebraic expression of the type x² + px + q, we find two factors a and b of q (i.e. the constant term) such that ab = q and a + b = p.
This is a true statement.

(2) "Division is the inverse of multiplication." This statement is true only in case of numbers, but it does not apply in case of division of algebraic expressions.
This is a false statement as ''division is the inverse of multiplication" is true in case of numbers as well as algebraic expressions.

(3) When we factorise an algebraic expression, we write it as a product of factors, where these factors may be numbers, algebraic variables or algebraic expressions.
This is also a true statement.

(4) When we multiply the expression enclosed in a bracket by a constant (or a variable) outside, each term of the expression has to be multiplied by the constant (or the variable).
This is also a true statement.

Question 19

1 / -0

Match the expressions given in column I with one of their factors given in column II.

Column I	Column II
(P) x³ - 1 - x + x²	(A) (x + 4)
(Q) x² + 5x + 4	(B) (3x + 2)
(R) -6x² - x + 2	(C) (x - 4)
(S) -6x² + 15x + 36	(D) (x - 1)

(P) - (D), (Q) - (A), (R) - (B), (S) - (C)

(P) - (D), (Q) - (B), (R) - (A), (S) - (C)

(P) - (C), (Q) - (A), (R) - (B), (S) - (D)

(P) - (D), (Q) - (C), (R) - (B), (S) - (A)

Solution

(P) x³ - 1 - x + x² = x³ + x² - x - 1

= x²(x + 1) - 1(x + 1) = (x² - 1)(x + 1) = (x - 1)(x + 1)(x + 1)

(Q)

(R) -6x² - x + 2

(S) -6x² + 15x + 36 = -3(2x² - 5x - 12)

Question 20
1 / -0

Do as directed.
(i) Factorise:
(ii) Find the greatest common factor of 10x²y³, 15x³y² and 25x⁴y⁵z.
(iii) Divide by .

A
(i) , (ii) , (iii)

B
(i) ,(ii), (iii)

C
(i) , (ii) , (iii)

D
(i) , (ii) , (iii)

Solution

(i) = = =

(ii) The greatest common factor of is because it divides each term.

(iii) = =

=

= So,